# Structure function tensor equations in inhomogeneous turbulence

Gatti, Davide 1; Chiarini, Alessandro; Cimarelli, Andrea; Quadrio, Maurizio
1 Institut für Strömungsmechanik (ISTM), Karlsruher Institut für Technologie (KIT)

## Abstract:

Exact budget equations for the second-order structure function tensor ⟨𝛿u$_{i}$𝛿u$_{j}$⟩, where 𝛿u is the difference of the i th fluctuating velocity component between two points, are used to study the two-point statistics of velocity fluctuations in inhomogeneous turbulence. The anisotropic generalised Kolmogorov equations (AGKE) describe the production, transport, redistribution and dissipation of every Reynolds stress component occurring simultaneously among different scales and in space, i.e. along directions of statistical inhomogeneity. The AGKE are effective to study the inter-component and multi-scale processes of turbulence. In contrast to more classic approaches, such as those based on the spectral decomposition of the velocity field, the AGKE provide a natural definition of scales in the inhomogeneous directions, and describe fluxes across such scales too. Compared to the generalised Kolmogorov equation, which is recovered as their half-trace, the AGKE can describe inter-component energy transfers occurring via the pressure–strain term and contain also budget equations for the off-diagonal components of ⟨𝛿u$_{i}$𝛿u$_{j}$⟩. ... mehr

 Zugehörige Institution(en) am KIT Institut für Strömungsmechanik (ISTM) Publikationstyp Zeitschriftenaufsatz Publikationsdatum 10.09.2020 Sprache Englisch Identifikator ISSN: 0022-1120, 1469-7645 KITopen-ID: 1000122221 Erschienen in Journal of fluid mechanics Verlag Cambridge University Press (CUP) Band 898 Seiten Art. Nr.: A5 Vorab online veröffentlicht am 25.06.2020 Schlagwörter turbulence theory Nachgewiesen in DimensionsScopusWeb of Science
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